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Two finite sets contain m and n elements, respectively. The first set has 112 more subsets than the second set. What are the values of m and n?
- 4, 7
- 7, 4
- 4, 4
- 7, 7
Correct answer: 7, 4
Solution
The number of subsets of a set with m elements is given by 2^m, and for a set with n elements, it is 2ⁿ. The equation 2^m - 2ⁿ = 112 holds true for m = 7 and n = 4, as it results in 128 - 16 = 112.
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